Thanks for posting that, although I never saw the Putt-Putt course, I did stay a the Orange Lake resort sometime in the lake 80's>
And I only glanced at the video for a few moments, but are those guys wearing golf shoes? (if so then LOL)
To answer the question, I would not allow this.
For a parent, it is a delicate situation -- I have taken my daughter to the range with me a few times a year for the last 3 or 4 years (she is 9 y.o. now) -- I basically make sure she is gripping it correctly and remind her to keep her feet "quiet" -- otherwise, I just let her hit and have fun. I think that if I tried to do too much, it would be counter-productive and she wouldn't be having fun. At this point, the critical thing in my opinion is a "decent" grip and letting her just groove hand-eye coordination by hitting the balls.
All that said, she has her first "official" lesson this Saturday with a girls group being taught by a local LPGA professional -- I am excited for her and as a bonus, I get to spend a full hour on the other side of the range hitting balls myself (which is not something I get to do all that much as a husband and father of young kids).